THE AID OF THE ACHROMATIC FRINGES. 11 



A correction must, however, be applied, since in the practical apparatus 

 the mirrors rotate at a fixed distance apart, zR. Hence the mirror N\ must 

 be displaced toward the right (shortening the path) by the normal distance. 



e=(R/cos aR) cos 45 



and the mirror AY toward the left by the same amount. The path-differ- 

 ence introduced is thus a decrement and is twice the 2 e cos (45 a) of each 

 mirror. Thus the total correction to be subtracted from the equation is 



4-R V/2 \/2 



~(i cos a) - - (sin a +cos a) - - = 2R(i cosa)(i-f tana) 



COS Oi 2 2 



Hence the equation becomes after reduction 



n\ = 2R (tan a i tan a-f-sin a-f-cos a) 

 or 



n\ = 2R (sin a + cos a i) 



To the second order of small quantities, if 2 = 45 is the angle of incidence 

 and AN the normal displacement of M', 



AAT i +A/2 

 =R 

 Aa cos i 



As all the mirrors receive the light on their silvered sides, M originally 

 compensates N if the mirrors are identical in thickness and glass. But 

 the transmission at (3) varies as the angle of incidence changes from 1 = 45 

 to 45 a. The glass path here decreases by 



e (sin i cos i tan r} Aa 



where e is the plate thickness, r the angle of refraction. The path-difference 

 as above reckoned has thus been increased by this amount, and this quantity 

 is to be added to the right-hand member. The effect will not usually ex- 

 ceed a small percentage of the air-path-difference and the ratio is the same 

 as above. 



4. Ocular micrometer. It has been stated that the motion of the fringes 

 across the field of the telescope (T, fig. 4) is astonishingly swift; hence it is 

 often desirable to insert a micrometer here, as the displacement of fringes 

 can thus be much more accurately and easily measured than at the 

 micrometer along the normal n of the opaque mirror M of the interferometer. 

 If the latter is of the type using an auxiliary mirror (mm, fig. 4) the fringes may 

 even be established of a size to correspond with the ocular micrometer by 

 rotating the auxiliary mirror; but this is not usually necessary. A good oc- 

 ular plate micrometer was at hand, dividing the width of field (about i cm.) 

 into 100 parts, the divisions being o.i mm. One-tenth of this is easily esti- 

 mated by the eye in view of the eye lens. The light from the collimator 

 SL should completely fill the field, a condition which may be fulfilled by 



